Finite Group Databasebeta

← Prev (#88268) Next (#88270) →

Cayley diagram

C139⋊C3 #88269

order417
isoclinismisoclinic class of C139⋊C3
automorphism?
homologyAbelianization (H1) = C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC139⋊C3

Splittings

Fitting, socle, derived, SylowC139 ⋊ C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC139C3
LCSG ▷ C139
UCSC1

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 139
transitive degreeμt(G) = 139

A minimal faithful permutation representation — 2 generators on 139 points:

(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,35)(18,27,32)(21,30,29)(23,33,26)(25,37,51)(28,40,48)(31,43,45)(34,46,42)(36,49,39)(38,53,70)(41,56,67)(44,59,64)(47,62,61)(50,65,58)(52,68,55)(54,72,91)(57,75,88)(60,73,85)(63,80,82)(66,83,79)(69,86,77)(71,89,74)(76,94,109)(78,95,106)(81,99,103)(84,101,100)(87,104,98)(90,107,96)(92,110,93)(97,113,122)(102,116,117)(105,118,115)(108,120,114)(111,123,112)(119,128,127)(121,129,126)(124,131,125)(130,135,134)(132,136,133)(137,139,138);(1,2,4,8,15,25,38,54,73,40,14,23,34,47,63,81,91,109,122,94,53,71,90,108,121,130,131,107,68,35,48,64,82,100,115,126,133,135,118,83,46,20,5,9,16,26,39,55,74,93,99,59,27,7,13,21,31,44,60,78,97,113,75,37,52,69,87,105,119,123,89,51,67,85,103,117,127,134,138,139,129,104,65,33,12,19,29,42,58,77,96,112,116,80,43,17,3,6,11,18,28,41,57,76,95,56,24,36,50,66,84,102,110,70,88,106,72,92,111,124,132,137,136,120,86,49,22,32,45,61,79,98,114,125,128,101,62,30,10)

Polycyclic presentation:

3,139|b^a=b^96

Conjugacy classes & character table

49 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD139⋊C3, C2×C139⋊C3, C3×C139⋊C3, …
maximal normal subgroup ofD139⋊C3, C2×C139⋊C3, C3×C139⋊C3, …
maximal quotient ofC2×C139⋊C3, C139⋊C9, C3×C139⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(417, 1);